Impulse response functions

The dynamic analysis was performed with impulse response functions. The short- run restrictions were imposed on reduced-form error terms u_t in (13.1) and (13.7). In case of non-linear TVAR model, the analysis is simplified in that the impulse responses are linear regime-dependent under the assumption that the regimes are highly persistent. Hence, for the piecewise linear VAR model in both regimes a standard impulse response analysis is performed.

In linear VAR models the responses change proportionally to the size of the structural shock. The responses are symmetrical with respect to positive and negative shocks, and they do not depend on the moment the disturbance occurs and the state of the economy at the moment of the shock. In order to be free of the restrictions in non-linear models, one may use non-linear impulse responses. Koop et al. (1996) have proposed the generalised impulse responses in which changes of the regimes are possible. Such impulse responses depend on the history of variables and the size and sign of the shock.

Empirical analysis Introduction

The Polish banking sector is interesting to investigate. It has a moderate size and simple structure, typical for emerging economies. It contains more than 60 commercial banks and branches of credit institutions. Banking sector assets account for more than 80% of GDP, loans as well as deposits 50% of GDP (Narodowy Bank Polski 2018). Banking activities are traditional as banks concentrate mainly on lending to local companies and households. Hence, the links between bank activities and macroeconomic developments are much more straightforward than in other developed banking sectors.

We model the dynamics of the macro-finance linkages in the Polish economy using a standard linear VAR model and a regime-switching threshold VAR model. The transition across two regimes is determined by the level of capital adequacy ratio (CAR). If this variable crosses a threshold, the economy shifts from a regime characterised by normal and tight capital standards. Hence, a threshold VAR model is employed to capture the asymmetries between the dynamics in the real and financial sectors.

In order to identify short-term shocks in both models, the Cholesky decomposition of the error covariance matrix and a fixed ordering of variables are adopted. For the selection of optimal lag-length, the assumption regarding stability

Table 13.1 VAR model variables

Source: The author’s own compilation.

conditions and Schwarz criterion is used. The statistical significance of individual parameter estimates was not examined; instead the focus was on IRFs, their uncertainty and economic interpretation.

The models were estimated for six variables (in the order) (see Table 13.1):

• • GDPSA
• • CPI
• • LOANS_R
• • WIBOR
• • IJLOANS
• • CAR

Variables are expressed in log-levels (GDPSA, CPI, LOANS_R) or levels (WIBOR, IJLOANS, CAR). For computations we used R Project for Statistical Computing and different packages: bookdown (Xie 2016), readxl (Wickham and Bryan 2018), xts (Ryan and Ulrich 2018), dplyr (Wickham et al. 2018), magrittr (Bache and Wickham 2014), ggplot2 (Wickham 2016), vars (Pfaff 2008a, Pfaff 2008b), tsDyn (Di Narzo et al. 2009; Stigler 2010), grid (R Core Team 2018), gridExtra (Auguie

• 2017) , kableExtra (Zhu 2018), kuitr (Xie 2014, 2015, 2018), stargazer (Hlavac
• 2018) , rmarkdown (Allaire et al. 2018; Xie et al. 2018), tidyverse (Wickham 2017).

It was assumed that the main channels of influence are credit and interest rate channels. Hence, the real credit for the non-financial sector and interest rates - WIBOR and loan rate - were included. WIBOR rate was intended to reflect the effects of monetary policy in the form of changes to the reference rate. It was assumed that the nature of WIBOR impact on the credit rate is more complex than the impact of the reference rate on WIBOR. Thus, two interest rates were included instead of three.